Question

Solve . 5x-49> or equal to 6-8(2x+7)
Write your solution using set builder notation.

Answer 1

This is a linear inequality. You can solve for x like you would a normal linear equation (it's linear in x since the highest power on any x is 1). The only time the direction of the inequality has to change (i.e. a flip in the inequality sign) is if you multiply or divide by a negative number.\[5x-49 \ge 6-8(2x+7)\]Expand the brackets on the RHS first,\[5x-49 \ge 6 - 16x-56\]Let's take all x's to the left-hand side, so add 16x to both sides,\[21x-49 \ge 6-56\]and collect all constants on the right (so add 49 to both sides),\[21x \ge -1\]Now divide both sides by 21 (this is a positive constant, so the direction of the inequality will remain the same),\[x \ge -\frac{1}{21}\]

Answer 2

set builder notation?

Answer 3

\[\left\{ x \in \mathbb{R} | x \ge -\frac{1}{21} \right\}\]

Answer 4

how do i write those symbols on computer

Answer 5

It depends on the software. Are you submitting something online?

Answer 6

yes

Answer 7

no software

Answer 8

It's difficult to say then. You can definitely use braces {} - they'll be somewhere on your keyboard. Unless there's a formula box or you know the computer language you're supposed to use, all you can really do is write,

{ x in R : x >=-1/21}

or something.

Answer 9

k ty

Answer 10

Or it might just accept {x >= -1/21}

Answer 11

o ok